I will get to this further below but first I should put forth the idea of creation of circular motion, laying aside the added complexities of the unison motion for a moment.
Creation of Circular Rotation
Now with B being unbalanced it will rotate and because B is at a slant relative to A it rotates as an ellipse on A. Remember though the direction of the rotation is initiated as per principle 15, not at an angle from the original linear motion. Now each new point of contact initiates a new “attempt” to accelerate A. This changes the direction and angle (relative to A) of the rotation of B, in its ellipse on A. It will, if A and B don’t separate first (#4 above) reach a point that it is perpendicular to A. At this point the “attempt/testing” to accelerate A is such that B will change to a circular rotation on A, and remain so. This point of circular rotation is reached at ¼ a revolution after impact, I believe.
A fundamental question: Does the linear motion stay “with” the rod (perpendicular) as it rotates, or is it pointed toward a direction in space? I would say the later, else if it shifts as the rod rotates then it would just make a big circle. I don’t have much reasoning on this, only it does appear it would work out better for the mechanics of the hypothesis. So I prefer the idea of motion being toward a horizon as when first initiated until stopped by an impending collision. So a principle,
Principle 16: Linear motion of a rod remains in its initial direction though space, without regard to any change in orientation of the rod toward that same direction, until impeded by impact.
Section 2: Collisions of two particles
Now to consider how two particles might normally collide, that is off center to each other. There are two basic ways these two particles might collide, via a direct hit, or by one overtaking another.
1. B could overtake A from many angles.
with many “slants” relative to A.
extent B has the velocity to overtake A, this excess velocity goes into torque of of B.
extent B has the velocity to overtake A, this excess velocity can go into a
of B around A.
5. At the same time of course B and A may be “sliding” relative to each other.
Here in step 3 B’s motion becomes a combination of linear motion, which keeps it in contact with A, and rotational motion
If a rod A was traveling in a linear motion and another rod B was traveling in the same direction with a combination of linear motion and rotational motion, it would appear when comparing the two side by side that the rotation of B would impede the linear direction of A if brought together with B overtaking and rotating on A. But this is not so as over each instance B is rotating off A it is displaced outward as an addition to the unison motion that is preserved. But in the case of B sliding by A due to the vectors at angles to each other, the unison motion established is only in the first instance. Then after rotation, although the displacement idea is fine, the added problem is with the linear motion of A and B different, the rotation causes an additional displacement of B relative to A that is a change from the established unison motion at the first instance. That is the rod B itself has changed position, so that its motion though space, unless the some as A, intersects A’s linear motion at different spots, even though B’s linear motion is in the same direction to the horizon as when established in the first instance. This can be seen most clearly when, as in figure 2-1, B comes to the top of A, it is now clearly moving up and off of A. Conversely if rotating to the bottom of A, all its linear motion is suppressed.
The fluctuations in motion can be broken down by quads as in figure 2-1. This all assumes a simple motion of one vector, for more than that see Appendix A, Section 4 for a fuller discussion. Diagram 2-1 is for rod B traveling bottom to top of page, impacting rod A in quad 3.
With a direct hit A-B, by Principle 10, both A and B will be off midpoints. All linear motion of each goes to torque and then rotation of each other.
One PP (A) will reach its midpoint before the other (according to their relative velocity’s and initial positions) where it will then transfer all its velocity into the (added) rotation of the other PP (A becomes stationary).
When that PP reaches its midpoint (both PP’s then are at a midpoint – midpoint contact) it will move in a linear direction moving each equal to ½ the velocity of its previous rotation (by Principle 9).